Polyhedral Prisms Research Articles

ЦИЛИНДРИЧЕСКИЕ АНИЗОТРОПНЫЕ МЕТАПОВЕРХНОСТИ С БИГРАДИЕНТНЫМ СПИРАЛЬНЫМ КОДИРОВАНИЕМ ФАЗЫ ПАНЧАРАТНАМ-БЭРРИ И АНОМАЛЬНЫМ РАССЕЯНИЕМ

Scattering characteristics of anisotropic cylindrical phase-gradient metasurfaces (MSs) with various helical Pancharatnam-Berry phase (PB-phase) coding are studied. The efficiencies of the scattering field reduction of circularly polarized (CP) waves in the forward half-space is compared for three different MS models with the same PB-phase gradient in the azimuthal direction and different phase gradients in the axial direction. The metasurfaces are conformally located on semi-cylindrical metallic polyhedral prisms. The meta-particles are of the form of triple coupled split-ring resonators. Spiral coding of the PB-phase of MS unit cells in the azimuthal and axial directions is carried out by the rotation of the meta-particles. The effect of constant phase gradients on the frequency characteristics of backscattered fields and bistatic diagrams of scattering of CP-waves in the azimuthal and meridional planes is numerically estimated. It is shown that the axial phase gradient causes more efficient anomalous scattering of co- and cross-polarized CP-waves. It leads to the deviation of intense diffraction lobes from the normal in the meridional plane by a large angle, with a shift of the lobes in the azimuthal plane. Bigradient MSs provide the scattering field reduction of CP-waves by at least 10 dB in the band from 10-12 GHz to 18.5 GHz in almost the entire forward half-space in the azimuthal plane and in the sector of angles up to ±45° in the meridional plane.

Measurement of Angles of Polyhedral Prisms on the State Primary Standard Get 22-2014 for a Flat Angle Unit

An installation for measuring the angles of polyhedral prisms is considered, in which autocollimators with digital registration of the coordinates of the optical mark are applied. Algorithms for solving systems of equations for the determination of angles by the method of aggregate measurements with the help of two and three autocollimators are described. The errors in the measurements are calculated and compared with the results of experimental measurements of the angles of polyhedral prisms.

Assessing and improving the accuracy of T-matrix calculation of homogeneous particles with point-group symmetries

We present an approach for improving the accuracy of T-matrix calculation of particles with point-group symmetries that eliminates from consideration some elements of the T matrix with low accuracy. A high accuracy approach (HAA) is suggested based on symmetry related comparative analysis of the accuracy rating of evaluation of surface integrals by the extended boundary condition method (EBCM).The symmetry relation for elements of the T matrix is a consequence of the general symmetry relation for particles with point-group symmetries. A simple comparative accuracy criterion composed of matrix norms rc(Q)=∥RgQ∥⋅∥Q−1∥ is suggested, where Q and RgQ are matrices computed with evaluation of surface integrals by the EBCM. An example of practical HAA application is given and results of numerical modeling of light scattering on finite polyhedral prisms are analyzed.

Minimal covers of the prisms and antiprisms

This paper contains a classification of the regular minimal abstract polytopes that act as covers for the convex polyhedral prisms and antiprisms. It includes a detailed discussion of their topological structure, and completes the enumeration of such covers for convex uniform polyhedra. Additionally, this paper addresses related structural questions in the theory of string C-groups.

Electron-Sponge Behavior and Electronic Structures in Cobalt-Centered Pentagonal Prismatic Co11Te7(CO)10and Co11Te5(CO)15Cluster Anions

The novel cluster anion [Co(11)Te(5)(CO)15]- ([3]-) has been isolated and structurally characterized as part of the salt [Cp*(2)Nb(CO)2][3] (Cp* = C(5)Me(5)). The cobalt-centered Co10 pentagonal prism is surrounded by a shell of two mu5-Te, three mu4-Te ligands, and 15 CO groups in terminal, symmetrical, and sigma-semibridging bonding modes. The hybrid carbonyl-telluride character of the ligand shell is reflected in the solid state by a one-dimensional assembly of polyhedral prisms along a backbone of [Cp*(2)Nb(CO)2]+ cations. Electrochemical studies reveal the presence of four redox couples of [3]n (n = -1 to -5). The electronic structures of various metal-centered and empty pentagonal-prismatic (PP) M10 clusters (M = Co, Ni) are calculated and compared to those of pentagonal-antiprismatic (PA) M10 structures. Closed-shells of 152 and 156 metal valence electrons, respectively, are found to determine the electronic structures and chemical properties of these geometries. From these considerations, magnetic properties have been predicted. They have been verified for the [Co(11)Te(7)(CO)10]- cluster anion, which exhibits a singlet-triplet gap of 0.318 kcal/mol.

Light scattering modeling of small feldspar aerosol particles using polyhedral prisms and spheroids

The use of simplified particle shapes for modeling scattering by irregularly shaped mineral-dust particles is studied using polyhedral prisms and spheroids as model particles. Simulated phase matrices averaged over shape and size distributions at wavelength 633 nm are compared with a laboratory-measured phase matrix of feldspar particles with known size distribution with effective radius of 1.0 μ m . When an equi-probable shape distribution is assumed, prisms and oblate spheroids agree with measurements to a similar degree, whereas prolate spheroids perform markedly better. Both spheroids and prisms perform much better than spheres. When an automatic fitting method is applied for finding optimal shape distributions, it is found that the most elongated spheroids are most important for good fits, whereas nearly-spherical spheroids are generally of very little importance. The phase matrices for the different polyhedral prisms, on the other hand, are found to be similar, thus their shape-averaged phase matrices are insensitive to the shape distribution assumed. For spheroids, a simple parameterization for the shape distribution, where weights increase with increasing departure from spherical shape, is proposed and tested. This parameterization improves the fit of most phase matrix elements attained with an equi-probable shape distribution, and it performs particularly well for reproducing the measured phase function.

Application of the extended boundary condition method to homogeneous particles with point-group symmetries

The numerical evaluation of surface integrals is the most time-consuming part of the extended boundary condition method (EBCM) for calculating the T matrix. An efficient implementation of the method is presented for homogeneous particles with discrete geometric symmetries and is applied to regular polyhedral prisms of finite length. For such prisms, an efficient quadrature scheme for computing the surface integrals is developed. Exploitation of these symmetries in conjunction with the new quadrature scheme leads to a reduction in CPU time by 3 orders of magnitude from that of a general EBCM implementation with no geometry-specific adaptations. The improved quadrature scheme and the exploitation of symmetries account for, respectively, 1 and 2 orders of magnitude in the total reduction of the CPU time. Test results for scattering by rectangular parallelepipeds and hexagonal plates are shown to agree well with corresponding results obtained by use of the discrete-dipole approximation. A model application for various polyhedral prisms is presented.

Method of calibrating polyhedral prisms using a single autocollimator

Method of calibrating polyhedral prisms using a single autocollimator

Modification of acetaminophen crystals. III. Influence of initial supersaturation during solution-phase growth on crystal properties in the presence and absence of p-acetoxyacetanilide

Acetaminophen (paracetamol, P) has been crystallized from aqueous solutions at various initial supersaturations (5.34–16.88 g dm −3) with 0 or 500 mg dm −3 p-acetoxyacetanilide (A) and its physical properties examined. In the absence of A, an increase in the initial supersaturation, σ (i.e. the initial concentration of P minus the solubility of P), does not appear to change the crystal habit (polyhedral prisms), but substantially increases the water content (by a factor of 8), decreases the enthalpy of fusion, ΔH f, melting point, T m, and entropy of fusion, Δs f, (by 6–14, 0.3–1.4 and 6–13 % respectively) and reduces the intrinsic dissolution rate of the crystals to constant values for σ between 6.63 and 14.32 g dm −3. On the other hand, when 500 mg dm −3 A are added to the solution, increasing the initial supersaturation broadens the crystal habit progressively, lowers and raises the water content, increases and decreases the ΔH f, T m and ΔS f, reduces the uptake of A to approximately constant mole fractions around 0.0013, and enhances and then reduces the intrinsic dissolution rate of the crystals to values about 50% greater than that of the polyhedral prisms grown in the absence of A. The above observations demonstrate the pharmaceutical significance of supersaturation during crystallization as a modulator of the physical properties and aqueous dissolution rate of the P crystals.

Modification of acetaminophen crystals. II. Influence of stirring rate during solution-phase growth on crystal properties in the presence and absence of p-acetoxyacetanilide

Acetaminophen (P) crystals have been grown from pure aqueous solutions containing 0 and 500 mg · dm −3 p-acetoxyacetanilide (A) at various stirring speeds (200–400 rpm) and the physical properties examined. When A is omitted from the solutions, an increase of the stirring rate has no significant effects on the crystal habit (polyhedral prisms), but markedly raises the water content (by a factor of 10), lowers the enthalpy of fusion, ΔH f, melting point, ( igT m) and entropy of fusion, ΔS f, (by 8–18%, 0 respectively) and decreases and then increases the intrinsic dissolution rate ( IDR) of the P crystals. However, in the presence of A, the crystals assume an acicular morphology, independent of the agitation rate of the solutions. Whilst eliciting no further changes in the habit of these crystals, application of more vigorous stirring to the solutions leads to a moderate decrease in the uptake of A, a slight increase in water content, a slight decrease in the ΔH f, T m and ΔS f as well as an initial reduction and a su IDR. Compared with the polyhedral prisms crystallized in the absence of A, these crystals invariably demonstrate a considerably higher IDR, consistent with their needle-like habit and much lower water content. These observations demonstrate the pharmaceutical significance of agitation during crystallization in modulating the physical properties and aqueous dissolution rate of the P crystals.

The use of polyhedral prisms for testing theodolites

The use of polyhedral prisms for testing theodolites

Automatic device for comparing polyhedral prisms

Automatic device for comparing polyhedral prisms

Some errors in calibrating polyhedral prisms

1. The results of the calibrations can be influenced by the systematic error in the “scale factor,” which is due not only to the calibration error of the readout device of the autocollimators, but also by the extent to which identical conditions are observed in the measurements. In addition, one of the parameters of a polyhedral prism, viz. the deviations of the angles between working faces from the nominal value, also exert an indirect effect on the correctness of the calibration results. 2. In view of the possibility of a progressive change in the “constant” angle between the line-up axes of the autocollimators, it is appropriate to select a modified method of measurements, by rotating the polyhedral prism in one direction only, in the structuring of the physical standard arrangement. When the method outlined here is employed, the possibility of that happening is established on the basis of the di values obtained, and the systematic error can be duly determined and eliminated. 3. The systematic errors cited in the article are not the only ones encountered in the calibration of polyhedral prisms. In a joint resolution adopted by PKS SEV in the field of angular measurements, the necessity of studying still other factors responsibility for errors in the measurements (effect of nonplanarity of the working surfaces accuracy in determining the plane of measurements, and so forth) is emphasized.

Standard apparatus for calibrating polyhedral prisms

On the basis of the results of a series of investigations into individual parts of the new standard installation, practical measurements, and the experience gained during these activities, we may state the following: The installation satisfies the main demands and principles of the project; as regards its parameters the installation stands on the same level as the best foreign installations of the same type; the installation will be able to be used, not only for the needs of the Czechoslovakian SSR, but also cooperatively by the member countries of the Socialist Economic Union — for example, in development of the theme set out in [5], in which the Czechoslovakian SSR is a coauthor.

Determination of the theodolyte graduation errors by means of polyhedral prisms

Determination of the theodolyte graduation errors by means of polyhedral prisms